Incipient fault amplitude estimation using KL divergence with a probabilistic approach

Abstract

International audienceThe Kullback–Leibler (KL) divergence is at the centre of Information Theory and change detection. It is characterized with a high sensitivity to incipient faults that cause unpredictable small changes in the process measurements. This work yields an analytical model based on the KL divergence to estimate the incipient fault magnitude in multivariate processes. In practice, the divergence has no closed form and it must be numerically approximated. In the particular case of incipient fault, the numerical approximation of the divergence causes many false alarms and missed detections because of the slight effect of the incipient fault. In this paper, the ability and relevance to estimate the incipient fault amplitude using the numerical divergence is studied. The divergence is approximated through the calculation of discrete probabilities for faultless and faulty signals. The estimation results that are obtained by simulation induce an error lower than 1% on the fault amplitude

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“…Numerous studies [5,16,17] have mentioned that the incipient fault should be characterized with the following features:…”

“…The developed SFI in (13) has three advantages over other related works. Firstly, it is more effective in detecting the change in mean deviation, while the methods in [16,17] are not capable because they used the assumption that Mathematical Problems in Engineering 5 ( −̃) is 0. Secondly, it can determine the sign of the faulty parameter, which is useful in the subsequent fault isolation.…”

Kernelized relative entropy for direct fault detection in industrial rotary kilns

“…Harmouche et al used PCA prefilter before executing the density estimation algorithm; however, data representation in the principal component subspace is still suboptimal unless normality is satisfied. Conventional techniques for reducing dimensionality are based on linear data transformations, which enforce normality resulting in a significant loss of information.…”

“…Although, the density ratio was proven to be an optimal statistical test in inferential statistics . Kullback and Leibler introduced the Kullback‐Leibler divergence (KLD) , or the statistical mean of the density ratio with respect to 1 density, which has been shown to be a good alternative to other statistics in change detection, and its detection performance when applied to different types of faults has been shown in many applications . The algorihm issues an alarm every time a probability density function (PDF) change from its reference version has occurred, which means that a fault can be indirectly detected through the PDF divergence.…”

“…Aggoune et al combined a black box identification method with the KLD for fault detection in a distillation column. The KLD was also employed in the work of Harmouche et al where the authors developed an analytical model for a bivariate process incipient faults magnitudes estimation.…”